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Power quality and stability have become the most important issues in power system operations, Micro Grids, and Smart Grids. Sensitive equipment can be seriously damaged when exposed to unstable power swing conditions. An unstable system may cause serious damage to Micro Grid System elements such as generators, transformers, transmission lines, and so forth. Therefore, out-of-step detection is essential for the safe operation of a Micro Grid system. In general, Equal Area Criterion (EAC) is a method for evaluating the stability of Smart Grid systems. However, EAC can be performed only if it is possible to analyze the active power and generator angle. This paper presents an analysis of the trajectory of complex power using a mathematical model. The variation of complex power is analyzed using a mathematical method, and then the relationship between complex power and EAC is presented, and a simulation performed. Later, in part II, a novel out-of-step detection algorithm based on part I will be presented and tested.

A Study on an Out-of-Step Detection Algorithm Using the Time Variation of Complex Power: Part I, Mathematical Modeling